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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Inner functions and the maximal ideal space of $H^{\infty }(U^{n})$


Author: S. H. Kon
Journal: Proc. Amer. Math. Soc. 72 (1978), 294-296
MSC: Primary 46J15; Secondary 32A35
DOI: https://doi.org/10.1090/S0002-9939-1978-0507326-X
MathSciNet review: 507326
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Abstract: For the case of the polydisc, Range has shown that the Shilov boundary ${\partial _n}$ of ${H^\infty }({U^n})$ is a proper subset of $\tau {X_n}$, the set of all restrictions of complex homomorphisms of ${L^\infty }({T^n})$ to ${H^\infty }({U^n})$. In this paper, we show that $\tau {X_n}$ is a proper subset of those complex homomorphisms of ${H^\infty }({U^n})$ which are unimodular on the class of all inner functions.


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Keywords: Inner functions, maximal ideal space, bounded analytic functions, polydisc, unimodular, closed subalgebra, <!– MATH ${L^\infty }({T^n})$ –> <IMG WIDTH="77" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${L^\infty }({T^n})$">
Article copyright: © Copyright 1978 American Mathematical Society